Minimal Stable Voting Rules

Abstract: In this paper, I characterize minimal stable voting rules and minimal self-stable constitutions (i.e., pairs of voting rules) for societies in which only power matters. To do so, I first let players' preference profiles over voting rules satisfy four natural axioms commonly used in the analysis of power: non-dominance, anonymity, null player and swing player. I then provide simple notions of minimal stability and minimal self-stability, and show that the families of minimal stable voting rules and minimal self-stable constitutions are fairly small. Finally, I conclude that political parties have evolved to ensure the minimal self-stability of otherwise not minimal self-stable constitutions.